Quantum communication through a partially reflecting accelerating mirror

Abstract

Motivated by the fact that the null-shell of a collapsing black hole can be described by a perfectly reflecting accelerating mirror, we investigate an extension of this model to mirror semi-transparency and derive a general expression for the corresponding Bogoliubov coefficients. In so doing, we introduce the concept of "impulsive accelerated mirrors", corresponding to those mirrors that are accelerated via an impulsive force. We show this treatment guarantees analytic solutions of Bogolubov coefficients for generic trajectories. In particular, we evaluate the corresponding particle production from the so-obtained Bogoliubov coefficients. Finally, we recognize the mirror as a Gaussian quantum channel acting between the spacetime regions of left-past and right-future. As a consequence we study the loss/amplification properties of this quantum channel, alongside the noise it creates, through which we evaluate its capacities in transmitting classical and quantum information.

Particle production by a relativistic semitransparent mirror in (1+3)D Minkowski spacetime

“…[16] for a perfectly reflecting mirror and in Ref. [17] for a partially reflecting mirror in The region on the mirror's right-hand side resembles that of gravitational collapse (See Fig. 1) except that there is nothing inside the future horizon (solid red line).…”